Making Truncated Wigner for dissipative spins 'plain easy'

Abstract: We put forward a user-friendly framework of the truncated Wigner approximation (TWA) for dissipative quantum many-body systems. Our approach is computationally affordable and it features a straightforward implementation. The leverage of the method can be ultimately traced to an intimate connection between the TWA and the semi-classical limit of the quantum Langevin equation, which we unveil by resorting to a path integral representation of the Lindbladian. Our approach allows us to explore dynamics from early to late times in a variety of models at the core of modern AMO research, including lasing, central spin models, driven arrays of Rydbergs and correlated emission in free space. Notably, our TWA approach outperforms the cumulant expansion method in certain models and performs comparably well in others, all while offering significantly lower computational costs and a much simpler formulation of the dynamical equations. We therefore argue that TWA could become in the near future a primary tool for a fast and efficient first exploration of driven-dissipative many-body dynamics on consumer grade computers.